You know all those annoying cleaning jobs? Where 30 dwarves are tied up for a month going to the entrance to pick up
one shoe, and then going all the way to the chasm to drop it, and then going back for a
mitten and so on?
I propose a method where an area or a room are tasked as one cleaning job, which is left to one dwarf to do. The first thing the dwarf does is to go to the store for an empty bin. The bin is then taken to the middle of the tasked cleaning area, whereupon the dwarf then goes around and picks up all the trash in the area and puts it in the bin.
After the trash is gone, or the bin is full, the dwarf goes to empty the entire bin at a time. Then, if there was more trash, it goes back to repeat the process. If not, it puts the bin back in the store.
One could even have a system with stationary bins that are set as trash receptacles. Dwarves will put trash there instead of the trash pile. Once in a while, haulers will haul the bin away to be emptied.